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Bargaining and Pricing in Networked Economic Systems University of Pennsylvania ScholarlyCommons Publicly Accessible Penn Dissertations Fall 2011 Bargaining and Pricing in Networked Economic Systems Tanmoy Chakraborty University of Pennsylvania, [email protected] Follow this and additional works at: https://repository.upenn.edu/edissertations Part of the Behavioral Economics Commons, Economic Theory Commons, Finance Commons, and the Theory and Algorithms Commons Recommended Citation Chakraborty, Tanmoy, "Bargaining and Pricing in Networked Economic Systems" (2011). Publicly Accessible Penn Dissertations. 445. https://repository.upenn.edu/edissertations/445 This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/445 For more information, please contact [email protected]. Bargaining and Pricing in Networked Economic Systems Abstract Economic systems can often be modeled as games involving several agents or players who act according to their own individual interests. Our goal is to understand how various features of an economic system affect its outcomes, and what may be the best strategy for an individual agent. In this work, we model an economic system as a combination of many bilateral economic opportunities, such as that between a buyer and a seller. The transactions are complicated by the existence of many economic opportunities, and the influence they have on each other. For example, there may be several prospective sellers and buyers for the same item, with possibly differing costs and values. Such a system may be modeled by a network, where the nodes represent players and the edges represent opportunities. We study the effect of network structure on the outcome of bargaining among players, through theoretical modeling of rational agents as well as human subject experiments, when cost and values are public information. The interactions get much more complex when sellers' cost and buyers' valuations are private. We design and analyze revenue maximizing strategies for a seller in the presence of many buyers, when the seller has uncertain information or no information about the buyers' valuations. We focus on developing pricing strategies, and compare their performance against truthful auctions. We also analyze trading strategies in financial markets, where a player quotes both buying and selling prices, again with uncertain or no information about future price evolution of the financial instrument. Degree Type Dissertation Degree Name Doctor of Philosophy (PhD) Graduate Group Computer and Information Science First Advisor Michael Kearns Second Advisor Sanjeev Khanna Keywords Theory and Algorithms, Computational Economics, Algorithmic Game Theory, Optimization, Computational Finance, Network Economics Subject Categories Behavioral Economics | Economic Theory | Finance | Theory and Algorithms This dissertation is available at ScholarlyCommons: https://repository.upenn.edu/edissertations/445 BARGAINING AND PRICING IN NETWORKED ECONOMIC SYSTEMS Tanmoy Chakraborty A DISSERTATION in Computer and Information Science Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy 2011 Supervisor of Dissertation Co-Supervisor Signature Signature Michael Kearns, Professor Sanjeev Khanna, Professor Computer and Information Science Computer and Information Science Graduate Group Chairperson Signature Jianbo Shi, Professor, Computer and Information Science Dissertation Committee Sudipto Guha, Professor, Computer and Information Science Ali Jadbabaie, Professor, Electrical and Systems Engineering Sampath Kannan, Professor, Computer and Information Science Eva Tardos, Professor, Computer Science, Cornell University (External) ABSTRACT BARGAINING AND PRICING IN NETWORKED ECONOMIC SYSTEMS Tanmoy Chakraborty Supervisors: Michael Kearns and Sanjeev Khanna Economic systems can often be modeled as games involving several agents or players who act according to their own individual interests. Our goal is to understand how various features of an economic system affect its outcomes, and what may be the best strategy for an individual agent. In this work, we model an economic system as a combination of many bilateral economic opportunities, such as that between a buyer and a seller. The transactions are complicated by the existence of many economic opportunities, and the influence they have on each other. For example, there may be several prospective sellers and buyers for the same item, with possibly differing costs and values. Such a system may be modeled by a network, where the nodes represent players and the edges represent opportunities. We study the effect of network structure on the outcome of bargaining among players, through theoretical modeling of rational agents as well as human subject experiments, when cost and values are public information. The interactions get much more complex when sellers’ cost and buyers’ valuations are private. We design and analyze revenue maximizing strategies for a seller in the presence of many buyers, when the seller has uncertain information or no information about the buyers’ valuations. We focus on developing pricing strategies, and compare their performance against truthful auctions. We also analyze trading strategies in financial markets, where a player quotes both buying and selling prices, again with uncertain or no information about future price evolution of the financial instrument. ii Contents 1 Introduction 1 1.1 ExpectationsfromaGoodModel........................ 2 1.2 Networked Bargaining . 4 1.2.1 BehavioralExperiments ......................... 5 1.2.2 Theoretical Modeling and Non-Linear Utility . 6 1.3 MechanismDesignandPricing ......................... 7 1.3.1 Limited Information Setting . 7 1.3.2 Bayesian Information Setting . 8 1.4 Pricing Strategies for a Financial Market Maker . 10 1.5 ConcludingRemarks............................... 11 2 Behavioral Study of Networked Bargaining 12 2.1 OverviewofResults ............................... 14 2.2 Background . 15 2.3 ExperimentalDesign............................... 18 2.3.1 Irregular Graphs . 19 2.3.2 Regular Graphs . 21 2.4 SystemOverview................................. 22 2.4.1 Human Subject Methodology . 24 2.4.2 SessionOverview............................. 24 2.5 Results....................................... 25 2.5.1 Social Welfare . 25 2.5.2 Nodal Differences............................. 27 iii 2.5.3 Comparison with Theoretical Models . 32 2.5.4 Human Subject Differences ....................... 33 2.6 Conclusion .................................... 36 3 Networked Bargaining with Non-Linear Utilities 37 3.1 OverviewoftheModel.............................. 38 3.1.1 Overview of Results and Techniques . 41 3.1.2 Related Work . 43 3.2 Preliminaries ................................... 45 3.2.1 Proportional Bargaining Solution (PBS) . 46 3.2.2 Nash Bargaining Solution (NBS) . 46 3.2.3 Stability and Equilibrium . 48 3.2.4 Bargaining Concepts as Nash Equilibria . 48 3.3 Linear Utility Functions: Characterizing All Equilibria . 49 3.4 Existence of Equilibrium for Non-Linear Utility Functions . 50 3.5 The Bargain Monotonicity Condition . 52 3.6 ComputingEquilibria .............................. 55 3.6.1 Algorithmic Results . 55 3.6.2 The Algorithm . 57 3.7 Inequality of Sharing in PBS vs NBS equilibria . 59 3.7.1 Inequality in NBS equilibrium . 59 3.7.2 InequalityinPBSequilibrium. 61 3.8 SimulationStudies ................................ 62 3.8.1 Methodology . 63 3.8.2 Correlation Between Degree and Wealth . 64 3.8.3 Regression Coefficients.......................... 64 3.8.4 Division of Wealth on Edges . 65 3.8.5 Other Utility Functions . 66 3.9 UniquenessofEquilibrium............................ 68 3.9.1 PBS Equilibrium is Not Unique . 68 3.9.2 NBS Equilibrium is Not Unique . 69 iv 3.9.3 Uniqueness in Regular Graphs . 69 3.9.4 Characterization of Bargain Rallying Condition . 70 3.10 Generalized Utility Functions . 72 3.11 Conclusion . 73 4 Item Pricing in Combinatorial Auctions 74 4.1 Preliminaries ................................... 82 4.1.1 Notation . 84 4.1.2 Optimal Social Welfare and Revenue Approximation . 85 4.1.3 The Single Buyer Setting with Uniform Pricing Strategies . 86 4.1.4 Optimizing with Unknown Parameters . 88 4.2 Improved Lower Bounds for Static Uniform Pricing . 89 4.2.1 A Hard Two-Player Instance . 90 4.2.2 Extensions of the Two-Player Instance . 93 4.3 Dynamic Uniform Pricing Strategies . 95 4.3.1 A Dynamic Uniform Pricing Algorithm . 95 4.3.2 Lower Bound for Dynamic Uniform Pricing . 99 4.3.3 Dynamic Monotone Uniform Pricing Strategies . 103 4.4 Static Non-Uniform Pricing . 107 4.4.1 Full Information Setting . 107 4.4.2 Buyers with -XOS Valuations . 108 4.5 Conclusion . 111 5 Sequential Posted Pricing in Multi-Unit Auctions 113 5.1 Preliminaries ................................... 116 5.1.1 Basic Result . 118 5.2 LP-based Algorithm for Large K . 119 5.2.1 Approximation Factor . 122 5.3 PTAS for constant K . 124 5.3.1 PTAS for Computing SPM . 125 5.3.2 PTAS for Computing ASPM . 129 v 5.4 Additional Details . 133 5.4.1 Discretization . 133 5.4.2 A Property of Poisson Distribution . 134 6 Market Making and Mean Reversion 135 6.1 A General Characterization . 140 6.2 Mean Reversion Models . 143 6.2.1 Ornstein-Uhlenbeck Processes . 145 6.2.2 The Schwartz Model . 148 6.3 TradingFrequency ................................ 150 6.4 Conclusion . 152 7 Summary of Results 153 7.1 Behavioral Study of Networked Bargaining . 153 7.2 Networked Bargaining with Non-Linear Utilities
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